Microscopic approaches to the nonlinear mechanics of driven crystals (NMDeRiC)

An accurate calculation of elastic and plastic properties of typical soft matter crystals (as they usually emerge in self-assembly processes of mesoscopic, colloidal particles) has been thoroughly studied over the past decades in the linear regime and under equilibrium conditions. These investigations have been carried out in detailed with theoretical approaches and were complemented and confirmed by numerous experimental studies. However, an extension of these investigations to the non-linear case and to non- equilibrium conditions (as they occur, for instance, in shear experiments) remains still in its infancy. It is the aim of this project to fill this gap by using three complementary theoretical approaches: (i) theoretical concepts of statistical mechanics, based on the projection operator formalism, (ii) classical density functional theory, and (iii) computer simulations. Since the impact of dislocations on these properties is meanwhile well understood, we will focus in our investigations on the role of point defects (such as vacancies, interstitial particle positions or multiply occupied lattice positions). The reason why we focus in our project on soft matter crystals is justified by the observation that such point defects occur very frequently in these systems, while - in striking contrast this is not the case for their hard matter counterparts; further, multiply occupied lattice positions have been shown to occur very often in crystals formed by (ultra-)soft particles. Our investigations will focus on the non-linear regime and on conditions out-of-equilibrium; such a scenario can, for instance, be imposed by external forces, as they occur in shear experiments, where the shear is transferred onto the crystal via the surrounding microscopic solvent. The above mentioned approaches are in their character and in their essence complementary; we thus count on strong effects of synergy in our joint efforts. We expect to obtain in this manner a profound understanding on how point defects can have an impact on the elastic and plastic properties of crystals beyond the linear regime and under non-equilibrium conditions.

MICROSCOPIC APPROACHES TO THE NONLINEAR MECHANICS OF DRIVEN CRYSTALS An accurate calculation of elastic and plastic properties of typical soft matter crystals (as they usually emerge in self-assembly processes of mesoscopic, colloidal particles) has been thoroughly studied over the past decades in the linear regime and under equilibrium conditions. These investigations have been carried out in detailed with theoretical approaches and were complemented and confirmed by numerous experimental studies. However, an extension of these investigations to the non-linear case and to non-equilibrium conditions (as they occur, for instance, in shear experiments) has remained in its infancy. In this project we have filled this gap by using three complementary theoretical approaches: (i) theoretical concepts of statistical mechanics, based on the projection operator formalism (Konstanz group), (ii) classical density functional theory (Tübingen group), and (iii) computer simulations in order to provide a route for predicting materials properties starting from the atomistic level (Vienna group). In the funding period we have investigated two simple, well-defined model systems, namely simple hard spheres and defect rich cluster crystals where the particles form clusters of overlapping particles which, in turn, are located on the equilibrium positions of FCC or BCC crystals. We have calculated for the very first time the direct correlation function of a hard sphere system. In contrast to to expectations this function is completely different from its liquid counterpart and is found to be defect dominated: in the limit of an ideal crystal it diverges and this divergent behaviour carries over to some of the generalized elastic constants. Further our joint efforts focused on the the linear elastic response of defect-rich crystals and the connection of this approach to the to the thermodynamics of deformation. We have found that for achieving the agreement between theory and simulations is the use of equivalent ensembles. The comparison of the elastic constant obtained via the theoretical framework and extensive computer simulations is highly satisfactory.